Problem: Solve for $x$ and $y$ using elimination. ${3x+6y = 69}$ ${-3x-5y = -60}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x+6y = 69}\thinspace$ to find $x$ ${3x + 6}{(9)}{= 69}$ $3x+54 = 69$ $3x+54{-54} = 69{-54}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {-3x-5y = -60}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(9)}{= -60}$ ${x = 5}$